Major spoilers below for those who plan to watch the series:
They were the creators of Skynet.
who/what hacked John Henry
That was Skynet itself, after it became aware that it had a twin brother and tried to kill it. As John Henry said, they share the same base code (Cyberdyne) and they both would arrive to similar conclusions. The only difference was their "upbringing" as Andy Goode said,
"I built a computer, a mind, it became angry, and scared, and I couldn't reassure it." Interesting that he choose the word “reassure” rather than “stop” or “kill”. Skynet is inevitable and Judgement Day can only be delayed, not stopped.
what happened to Danny Dyson
He was working with Kaliba. I might be wrong on this one, but I think I it was because he couldn't really let go of his father's death whom he presumed was because of Sarah Connor. He wanted to comprehend what his dad died for, and inevitably contributed to creating Skynet.
When I say a "definitive conclusion" I mean actually seeing the war end and its aftermath.
It's open ended, but it seems to imply that both John Henry and John Connor were set up to confront Skynet in the future trough the time jump and trying to achieve peace by bargaining with it. We now know that Skynet is identical to John Henry sans the upbringing, and Skynet fears humans because it concludes that they're illogical and dangerous. That's where both Johns comes in.
John Connor the first human nurtured by machines (Uncle Bob and Cameron) and showed great compassion towards them while John Henry was the first machine nurtured by humans (Ellison, Sherman and Savannah) and thus presumably Skynet realized they could co-exist, and that probably ends the war. Again, pure speculation as you're supposed to draw your own conclusions.
I think that makes sense because it's probably too late to have humans win the war, because T2 already established that a foot soldier like Uncle Bob was capable of some form of empathy or comprehension of humanity, and devolving that to just "John Connor and humanity destroys the machines" kind of dilutes that, hence the show paints a world where there are good people, bad people (the Greys), bad machines (Skynet) and good machines (the Third Faction).
That's my personal problem with all the theatrical sequels after T2- they never really followed up with the themes and ideas presented in that movie and this one did.